On the existence, uniqueness and stability of solutions for semi-linear generalized elasticity equation with general damping term
The paper deals with a semi-linear hyperbolic boundary value problem for linear elastic equations with general damping term and nonlinearities of variable exponent type. The author introduces function spaces of Sobolev type with variable exponent. Then the author proves local and global existence theorems for the weak solution. The proof is based on the Galerkin's approximations. The uniqueness of this solution is obtained by eliminating some auxiliary conditions that have been imposed by other specialists. The author shows also that any solution with nontrivial initial datum becomes stable.
scientific article; zbMATH DE number 6819825
scientific article